Nonlinearity-induced transition in heat conduction through a topological metamaterial of rotors

TL;DR

This paper studies heat conduction in a chain of rotors, revealing a transition from insulating to ballistic conduction at a topological phase transition, and normal diffusive conduction in nonlinear regimes.

Contribution

It demonstrates how nonlinearity and topology influence heat conduction, extending the topological insulator concept to thermal transport in rotor chains.

Findings

Linearized model shows exponential decay of heat current with chain length in topological phases.

At the topological phase transition, the chain conducts heat ballistically.

Nonlinear chain exhibits normal diffusive heat conduction across phases.

Abstract

We investigate heat conduction in a one-dimensional chain of rigid rotors. The rotors are constrained to rotate in a plane about fixed pivot points and coupled by springs, such that in equilibrium, the neighboring rotors lie on opposite sides of the chain axis. The linearized limit of this model valid for small angular displacements, was first introduced by Kane and Lubensky (KL) as a topological mechanical insulator hosting zero-energy vibrational edge modes. We show that the linearized KL chain behaves as a thermal insulator at low temperature in both the topological phases with a finite band gap, and the heat current falls exponentially with the chain length. When the gap vanishes at the topological phase transition, the KL chain becomes a good thermal conductor and conducts heat ballistically. The chain of rotors for arbitrary angular displacements hosts nonlinear solitary waves and distinct topological mechanical phases. Our numerical analysis shows normal (diffusive) heat conduction in all topological phases of the nonlinear chain. Nevertheless, a finite thermal conductivity is achieved for different system sizes in different topological phases of this nonlinear chain.